Blockchain networks, which can also be referred to as blockchain systems, consensus networks, distributed ledger system networks, or blockchain, enable participating entities to securely and immutably store data. A blockchain can be described as a ledger of transactions and multiple copies of the blockchain are stored across the blockchain network. Example types of blockchains can include public blockchains, consortium blockchains, and private blockchains. A public blockchain is open for all entities to use the blockchain, and participate in the consensus process. A consortium blockchain is a blockchain where the consensus process is controlled by a pre-selected set of nodes such as certain organizations or institutions. A private blockchain is provided for a particular entity, which centrally controls read and write permissions.
Blockchains can use different record-keeping models to record transactions between users. Example record-keeping models include the unspent transaction output (UTXO) model and the account balance model. In the UTXO model, each transaction spends output from prior transactions and generates new outputs that can be spent in subsequent transactions. A user's unspent transactions are tracked, and a balance that is available to spend is calculated as the sum of the unspent transactions. In the account balance model, each user's account balance is tracked as a global state. For each transaction, a balance of a spending account is checked to make sure it is larger than, or equal to, the transaction amount. This is comparable to traditional banking.
A blockchain includes a series of blocks, each of which contains one or more transactions executed in the network. Each block can be analogized to a page of the ledger, while the blockchain itself is a full copy of the ledger. Individual transactions are confirmed and added to a block, which is added to the blockchain. Copies of the blockchain are replicated across nodes of the network. In this manner, there is global consensus on the state of the blockchain. Further, the blockchain is open for all nodes to see, at least in the case of public networks. To protect privacy of blockchain users, encryption technologies are implemented.
Under the account balance model, commitment schemes can be used to hide values that both parties of a transaction commit to. Commitment schemes can arise out of the need for parties to commit to a choice or value, and later communicate that value to the other parties involved. For example, in an interactive Pedersen commitment (PC) scheme, a first user can commit to a transaction amount t by sending a commitment value PC(t, r) that is generated based on random value r. The commitment value is generated, and a second user can only reveal the transaction amount t by obtaining the random number r. To ensure that the transaction amount is valid, a range proof can be created to prove that the transaction amount is greater than or equal to zero and less than or equal to the account balance.
In some cases, multiple transactions can be made from a user. Because the range proof is associated with the remaining balance of the account, the multiple transactions need to be verified sequentially in the blockchain. As such, the corresponding range proofs can be correctly associated with the remaining balances of the account after each transaction. However, verifying multiple transactions sequentially can be time-consuming. A record-keeping model that allows parallel verifications of transactions would be advantageous especially for time-sensitive tasks.